Cults were belief-based organisations, often having smaller numbers than religions, which focused on the worship of deities or were formed with a goal or purpose for their organisation. They were often viewed to have 'unusual' beliefs when compared to other religions.
Many cults were formed for specific goals or purposes. The Cult of Skaro was a cult formed during the Last Great Time War by a group of Daleks to think in manners outside that of the Dalek race. (TV: Doomsday) The Cult of Shining Darkness was formed with the purpose of destroying all robotkind. (PROSE: Shining Darkness)
Other cults were much like religions, formed for/through the worship of a deity; on Earth most such cults took their name from the deity they worshipped. These included the Cult of Vulcan (TV: The Fires of Pompeii), the Brotherhood of Demnos (TV: The Masque of Mandragora) and the Hecate Cult. (TV: A Girl's Best Friend) One cult worshipped Bernice Summerfield as a deity from its church on a deserted aircraft carrier at the centre of the Medelein Sea on Phraxa. They instigated a galaxy-wide campaign to bring about her death because she wasn't living up to their image of her. (PROSE: The Dead Men Diaries)
Other cults had specific places within their respective societies. The Sibylline Sisterhood was a highly prestigious cult of soothsayers in Pompeii that cultivated the psychic potential of individuals present in the city. (TV: The Fires of Pompeii) The Tong of the Black Scorpion, who worshipped Weng-Chiang, was described by the Fourth Doctor as one of the most dangerous criminal organisations on Earth. (TV: The Talons of Weng-Chiang)
Other cults such as Faction Paradox revelled in being known as a "cult", as a taboo and as an affront to the Time Lords, whose ideologies and practices they actively sought to mock and intimidate. (PROSE: Alien Bodies, Unnatural History)
On Earth, cults such as the Black Coven and Cabal of the Horned Beast integrated elements of the occult into their practices, along with creating a "secret society" around their cult. (PROSE: Timewyrm: Exodus, The Severed Man, Child of Time)